Problem of the Week 8

This is the 8th problem of the week of MTAP Reviewer.

Problem

The diagonal of a square is 6cm. Find the area of the square that is twice its size.

Solution

We can divide a square into several ways, one of which is using its diagonal.

square
Click on the image to enlarge

Now, using the diagonal of the square as side of the larger square, we can create a larger square as shown above. As seen, the diagonal of the square cuts the square into half. This half region makes a fourth of the larger square (Can you see why?).

Since the length of the side of the larger square is the diagonal of the smaller square 6, the area of the larger square is 6× 6 = 36.